A279290 Sum of cubes of nonprime divisors of n.
1, 1, 1, 65, 1, 217, 1, 577, 730, 1001, 1, 2009, 1, 2745, 3376, 4673, 1, 6778, 1, 9065, 9262, 10649, 1, 16345, 15626, 17577, 20413, 24761, 1, 31592, 1, 37441, 35938, 39305, 42876, 55226, 1, 54873, 59320, 73577, 1, 86310, 1, 95897, 95230, 97337, 1, 131033, 117650, 141626, 132652, 158249, 1, 183925, 166376
Offset: 1
Examples
a(4) = 65 because 4 has 2 nonprime divisors {1,4} and 1^3 + 4^3 = 65.
Links
Programs
-
Mathematica
Table[DivisorSum[n, #1^3 & , !PrimeQ[#1] & ], {n, 55}] Table[DivisorSigma[3, n] - DivisorSum[n, #1^3 & , PrimeQ[#1] & ], {n, 55}] Table[Total[Select[Divisors[n],!PrimeQ[#]&]^3],{n,60}] (* Harvey P. Dale, Aug 02 2024 *) -
PARI
a(n) = {my(f = factor(n)); sigma(f, 3) - sum(i=1, #f~, f[i, 1]^3);} \\ Amiram Eldar, Jan 11 2025